If the gravitational potential is given by $V = (3x + 4y + 12z) \ J/kg$,then the gravitational intensity at the point $(x = 1, y = 0, z = 3)$ is ....... $N \ kg^{-1}$.

Two masses $90 \ kg$ and $160 \ kg$ are separated by a distance of $5 \ m$. The magnitude of the intensity of the gravitational field at a point which is at a distance $3 \ m$ from the $90 \ kg$ mass and $4 \ m$ from the $160 \ kg$ mass is (Universal gravitational constant,$G=6.67 \times 10^{-11} \ N \ m^2 \ kg^{-2}$)

Find the gravitational force of attraction between the ring and the sphere as shown in the diagram. The plane of the ring is perpendicular to the line joining the centres. The distance between the centres of the ring (mass $m$) and the sphere (mass $M$) is $\sqrt{8}R$,where both have an equal radius $R$.

Two bodies of mass $100 \ kg$ and $10^4 \ kg$ are lying one meter apart. At what distance from the $100 \ kg$ body will the intensity of the gravitational field be zero?

$A$ spherical shell is divided into two parts. If the gravitational intensity at point $P$ due to the upper part is ${I_1}$ and due to the lower part is ${I_2}$,then:

If a cavity is made inside a solid sphere,then the gravitational field inside the cavity is